Advisors: The ‘7 Most Important Equations’ on Retirement

Moshe Milevsky, below right, is a household name to financial advisors. Indeed, the York University finance professor and author of several well received books and innumerable articles, academic and popular, has become a rock star on the advisor lecture circuit. Why?

It is Milevsky’s unique approach that has made him, in many advisors’ opinion, one of the most important educators on retirement finance today.

There are other experts whose level of knowledge may equal Milevsky’s, yet they can’t seem to explain retirement income without bashing the people—financial advisors, that is—who help ordinary Americans achieve their retirement plans.

Milevsky speaks to advisors without condescension and with a rare facility for taking abstract mathematical concepts and making them comprehensible to practitioners. In other words, he makes you smarter and more capable as a professional.

And that is why financial advisors will particularly benefit from reading and thoroughly digesting his book to be released in June, which Research and AdvisorOne have previewed on a heavily excerpted basis since January.

Called “The 7 Most Important Equations for Your Retirement,” the book inculcates key principles of retirement finance—a subject that is not intuitive in the way that accumulation-based investing is—while readers think they are being entertained. Milevsky knows how to put just enough sugar into the mix to mask the pain of mathematics for the math-averse. For those who are quantitatively oriented, the virtuoso treatment of the geniuses who have achieved equation immortality is a connoisseur’s delight.

The first of these immortals is Fibonacci, who 800 years ago introduced the methodology for solving complicated questions involving interest rates known as present value analysis.

Milevsky shows how, by bringing all cash flows to a common point in time, Fibonacci was able to eliminate the messy time dimension involved in compound interest calculations. Through this technique, financial advisors can now mathematically evaluate the question of how long their clients’' savings will last in retirement.

Besides determining how long a certain sum of money will last, retirement planners will also find it useful to assess how long a client’s money should last. For that Milevsky turns to Benjamin Gompertz’ Law of Mortality.

This equation brings sophistication and discipline to a process that is all too often ad hoc. “I have observed that when financial advisors discuss retirement income planning with their clients, they start by asking questions about how long they would like to plan for,” Milevsky writes.

But, he adds, “life is random, and you know it.” Thus, the scientific approach to retirement income planning requires a knowledge of the odds of living to various ages, and a realistic plan that considers how to adjust spending in the event the client lives to a very old age.

By tinkering with mortality tables, Gompertz discovered that the difference in the natural logarithm of death rates was constant with age. While the date of your client’s death is unknown, Milevsky shows that, thanks to Gompertz, we can determine the probability your client will survive to any given age and plan accordingly.

An understanding of life probabilities is one key component to helping clients evaluate a simple but common question: Should your retiring client take a lump sum or keep an annual pension? For that question, Milevsky turns to Edmond Halley, best known as the astronomer for whom an important comet that visits our atmosphere now and then is named.

Milevsky discusses in fascinating detail how the astronomer’s pivotal contribution to retirement finance may have something to do with the mystery of how his aristocratic father was likely murdered and found dead and completely naked except for his shoes, floating in the river in England in 1684. That is a typical example of how Milevsky manages to keep a book on retirement finance riveting.

But for our purposes, Halley’s sudden interest in mortality rates led to an equation that calculates what a pension annuity is worth. And that can help advisors quickly determine if their client is better off taking their money out of a retirement plan and buying their own annuity. A simple calculation—based on current market interest rates—shows you whether the pension is a good deal or not.

Once your clients have their retirement stash, a critical question is how much they can spend, and for that Milevsky walks the reader through Irving Fisher’s optimal retirement plan. Financial planners ought to be more familiar with the early 20th century economist’s work, since he utterly refuted the almost bedrock idea among financial planners of the “4 percent rule,” i.e., that your client can safely withdraw 4percent of their portfolio a year.

Fisher’s equation tells you how to consume in retirement based on how much of a chance the client is willing to take on living longer than expected. This is based on the client’s subjective personal preferences and attitude toward risk. Fisher taught that there is no shame in spending more early in retirement (as was then thought to be the case), to which Milevsky comments: “Personally, I suggest that if you are worried about living to 100 with no money, wandering the streets panhandling and in search of soup kitchens, get yourself a pension annuity!”

Another critical question retirement advisors face is how much of a client’s funds should be invested in risky stocks versus safe cash. And for that Milevsky turns to the late 20th century economist Paul Samuelson, who took an axe to the “stocks for the long run” argument that Wall Street loudly promotes.

Samuelson showed how the idea that risk dissolves over longer stretches of time was based on poor math that made the stock market look like a casino that actually heavily favors the gamblers. He demonstrated that the optimal amount of stocks versus safe cash was “time-invariant”—that a declining probability of shortfall was offset (exactly, mathematically) by the enormous disutility of a loss.

While time is not a factor in Samuelson’s equation, it is implicitly a factor in retirement decisions because of the time-based diminution of human capital, an idea that actually lies at the heart of Solomon Huebner’s equation. Huebner, the father of insurance economics, brought human capital valuation into a field that had previously lacked discipline. Decisions about how much insurance should be owned were typically ad hoc and arbitrary.

Huebner’s equation answered the difficult question of how you derive a present value for the money the insured’s beneficiaries will receive at some random time in the future.

He also explained the importance of policyholders’ converting their insurance into life annuities around the age of retirement. Writes Milevsky: “I venture to guess that if Professor Huebner were alive today, he would be on the road with annuity wholesalers giving seminars to financial advisors and their clients, extolling the virtues of longevity insurance and life annuities.”

The seventh and final equation in Milevsky’s book was that of the Soviet-era Russian mathematician Andrey Nikolaevich Kolmogorov. Milevsky writes of the winner of the 1941 Stalin Prize: “It is…a supreme irony that financial advisors…owe Professor Kolmogorov an incalculable debt of gratitude. You see, his work on probability theory…created the foundations upon which all retirement income planning software is now based.

“Every time an Armani-wearing stock broker runs a ‘Monte Carlo simulation’ to help a client achieve their very non-socialist goal of retiring rich, they must thank Andrey Nikolaevich.”

This review gives just a little taste of what advisors can learn by reading Milevsky’s book. The key idea advisors should take away is that true understanding of retirement planning is enhanced by understanding not only how things work, but why they do. Milevsky’s book will deepen your knowledge and explanatory power. That is why it is one of the most important books that a retirement advisor must read.